Class 3: More on evaluation
SI 413 - Programming Languages and Implementation
Dr. Daniel S. Roche
United States Naval Academy
Fall 2011
Roche (USNA)
SI413 - Class 3
Fall 2011
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Scheme is lists!
Everything in Scheme that looks like a list is a list.
You have been using lists, but usually asking Scheme to evaluate them.
Scheme evaluates a list by using a general rule:
First, turn a list of expressions (e1 e2 e3 ...) into a list of atoms
(a1 a2 a3 ...) by recursively evaluating each e1, e2, etc.
Then, apply the procedure a1 to the arguments a2, a3, . . .
Anything that is not a list (i.e., an atom) just evaluates to itself.
Roche (USNA)
SI413 - Class 3
Fall 2011
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Special Forms
The only exceptions to the evaluation rule are the special forms.
Special forms we have seen: define, if, cond, and, or.
What makes these “special” is that they
do not (always) evaluate (all) their arguments.
Example: evaluating (5) gives an error, but
(if #f (5) 6) just returns 6 — it never evaluates the “(5)” part.
Roche (USNA)
SI413 - Class 3
Fall 2011
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Scheme evaluation and unevaluation
We can use the built-in function eval to evaluate a Scheme expression
within Scheme!
Try (eval (list + 1 2))
Roche (USNA)
SI413 - Class 3
Fall 2011
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Scheme evaluation and unevaluation
We can use the built-in function eval to evaluate a Scheme expression
within Scheme!
Try (eval (list + 1 2))
We can also ask Scheme not to evaluate an expression by using the special
form quote.
Try (quote (+ 1 2))
Roche (USNA)
SI413 - Class 3
Fall 2011
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Quoting
There is a convenient shortcut of quote: Putting an apostrophe before
the expression-to-be-quoted.
For example, ’(1 2 3) is the same as (list 1 2 3).
This gives us a synonym for null: ’().
In fact, ’() is the preferred Scheme way of writing an empty list.
Creating nested lists also becomes trivial:
’(1 (2 3) 4) is equivalent to (list 1 (list 2 3) 4)
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SI413 - Class 3
Fall 2011
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Symbols
An unevaluated identifier is called a symbol.
(Note: the predicate symbol? is useful here.)
Symbols are useful beyond evaluation and quoting.
We often use them like ENUMs in C++.
Examples: units, months, grades
Symbols are often used to tag data: (cons 10.3 ’feet)
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Some exercises
1
Write a function sign that takes a number and returns the symbol
’positive, ’negative, or ’zero, as appropriate.
2
Write a simple quoted expression that is equivalent to
(cons (cons 3 (cons ’q null)) (cons ’a null)).
3
Write a function that takes a list of numbers and adds them up using
the + function. (Hint: first build this expression using cons, then
evaluate it using eval.)
4
Repeat #3 using the built-in apply function.
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SI413 - Class 3
Fall 2011
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The need for local variables
This code finds the largest number in a list:
(define (lmax L)
(cond [(null? (cdr L)) (car L)]
[(>= (car L) (lmax (cdr L))) (car L)]
[else (lmax (cdr L))]))
Roche (USNA)
SI413 - Class 3
Fall 2011
8 / 10
The need for local variables
This code finds the largest number in a list:
(define (lmax L)
(cond [(null? (cdr L)) (car L)]
[(>= (car L) (lmax (cdr L))) (car L)]
[else (lmax (cdr L))]))
This has worst-case exponential running time!
We need a way to save the value of (lmax (cdr L)).
Roche (USNA)
SI413 - Class 3
Fall 2011
8 / 10
The let special form
Scheme provides let as a way to re-use temporary values:
(define (lmax L)
(if (null? (cdr L))
(car L)
(let ((rest-max (lmax (cdr L))))
(if (>= (car L) rest-max)
(car L)
rest-max))))
Note the extra parentheses — these allow multiple temporary variables:
(let ((a 5) (b 6)) (+ a b)) ⇒ 11
Roche (USNA)
SI413 - Class 3
Fall 2011
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More exercises
1
Write a Scheme expression that computes the formula
5x 2 y + 3xy − x + 4y at the point (x, y ) = (1.5, 2.5).
2
Write a Scheme function (f x y) that computes the formula
5x 2 y + 3xy − x + 4y at any given point.
3
Simulate the following Java code as a series of nested lets:
int x = 1;
x += 3;
x *= 12;
return x;
Roche (USNA)
SI413 - Class 3
Fall 2011
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